Robust finite-time synchronization of coupled harmonic oscillations with external disturbance

This paper considers the problem of finite-time synchronization for multiple coupled harmonic oscillators with a leader-follower architecture. By using the techniques of finite-time control and saturation control, a class of bounded finite-time state feedback controllers are first proposed. Then to address the case in the presence of external disturbance and lack of velocity measurement, a finite-time convergent observer is constructed to estimate both the unknown velocity information and the disturbance in a finite time. Finally, a disturbance observer-based bounded finite-time output feedback controller is developed. Rigorous proof shows that the systems output can reach synchronization in a finite time and the final consensus states are the leader׳s states.